This is a one semester course on ordinary differential equations and linear algebra. The goal will be to cover the standard theory (tricks for solving simple equations and the theory of linear systems) quickly enough so there is time to some consider qualitative methods for studying nonlinear systems. Many examples will be treated and there will be two computer lab sessions.

Differential Equations and their Applications (4th ed.), by Martin Braun. We will follow the topics in the book fairly closely but sometimes the lectures will cover extra topics (indicated by xt below).

Homework / Quizzes | 20 % |

Midterm Exams (20 % each) | 40 % |

Final Exam | 40 % |

Midterm I | Tuesday, October 5 |

Midterm II | Tuesday, November 9 |

Final | Friday, December 17 |

Week |
Topic |
Reading |

9/8-9/10 | Simple 1st order equations, applications | 1.2, 1.4, 1.8 |

9/13-9/17 | Existence theory, qualitative theory | 1.10, xt |

9/20-9/24 | Numerics, Lab I, 2nd order linear equations | 1.13, 1.16, 2.1, 2.2 |

9/27-10/1 | Forced 2nd order linear eqs., oscillators | 2.3-2.6, 2.15 |

10/4-10/8 | Review, Midterm I, series solutions | 2.8 |

10/11-10/14 | Laplace transforms, delta functions | 2.9-1.12 |

10/18-10/22 | Vector spaces, dimension | 3.1-3.4 |

10/25-10/29 | Determinants | 3.5, 3.6 |

11/1-11/5 | Linear equations and transformations | 3.6, 3.7 |

11/8-11/12 | Review, Midterm II, eigenvalue method | 3.8, 3.9 |

11/15-11/19 | Matrix exponential | 3.10, 3.11 |

11/22-11/14 | Variation of parameters | 3.12 |

11/29-12/3 | Equilibria and the phase plane | 4.1-4.4 |

12/6-12/10 | Periodic orbits, applications, Lab II | 4.6-4.8 |

12/13-12/15 | Lorenz equation and chaos | xt |